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Friday, September 25, 2009

Annualized standard deviation ...yes!

Okay, so the decision has been made: effective January 2011, GIPS compliant firms must report a 36-month annualized standard deviation, on an annual basis (that is, for all years starting with 2011). Further clarity is in order.

First, is standard deviation risk? There is hesitation to call it that, because a lot of folks don't consider it risk. But if it's not risk, why show it? Granted, not everyone thinks of volatility as being a risk measure, but most firms report that they use standard deviation as a risk measure. If volatility isn't risk, then is volatility such a valuable measure that we need to see it reported?

I think it's a mistake NOT to call standard deviation risk: the fact that not everyone agrees shouldn't be a reason not to. There is disagreement about much of the standards, but that doesn't stop these items from being included. It's even more confusing not to call standard deviation risk. Is someone going to be offended if we call it "risk"? I think not.

Is the Sharpe ratio a risk measure? Technically it's a risk-adjusted return. And, what risk measure is used to adjust the return? Yes, you're right: standard deviation. But if standard deviation isn't risk, then I guess the Sharpe ratio can't be a risk-adjusted measure. Who's going to tell Bill?

Okay, and so HOW do we calculate standard deviation? First, use 36 months ... not days, not quarters, not years: months! You will also be required to include the annualized return for each 36 month period. What if you don't have 36 months' of composite returns? Then don't show this until you do (well, actually, you arguably can show a standard deviation for the period you have, but you're not required to until you reach 36 months).

Do we divide by "n" or "n-1" (where "n" is the number of months (i.e., 36))? No decision has been made yet, though it appears from comments at this week's conference that "n" might win out. We use "n" for the population and "n-1" for a sample; some might argue that it would be wrong to use "n," while others would argue that it's wrong to uses "n-1." This is debatable and controversial, no doubt. And, no doubt more details will follow.

7 comments:

The Journal of Performance Measurement 50th issue also mentioned about Treynor Ratio (don't subscript but got a free copy from my friend). This could also be consider a risk adjusted return equation. Are we going to assuem BETA as a form of risk as well?

If we start saying or writing SIGMA as a form or risk, I have a feeling someday a sophisticated investor (not financial savvy but just a lot of money) may bring a legal case and try to use SIGMA as a way to prove negligent caused by the defendant.

There is a larger ethical issue here: according to the CFA Institute's own ethics guidance, one must present BOTH the return and the risk of an investment. One cannot present return without its accompanying risk. To do so would violate an underlying principle of "informed consent" which requires fair representation and full disclosure of all material facts. Fair representation and full disclosure are also the basis for GIPS.

So why does it take a committee years to catch up to the ethical guidance that has been in place for decades? And why so much debate simply to recommend showing the most basic risk statistic which provides a reasonable measure of the potential uncertainty around an investment's return? The performance industry might take this opportunity to examine why it is so prone to debate the nuances of various risk measures while it delays presenting any information whatsoever about the risk of investments. "Half a loaf is better than none" and a reasonable risk measure that enjoys almost universal acceptance (although admittedly not the complete or perfect measure) is surely better than leaving investors completely in the dark about risk.

We've been "fiddling while Rome burns" and "rearranging the deck chairs on the Titanic" in this ongoing debate about including a risk measure in a GIPS presentation of performance. This decision to include standard deviation as a required risk measure is LONG overdue. Managers can and should present additional information about risk that is material and representative of their investment product. THAT is the proper forum for all this debate. Frankly, it was wrong to delay the presentation of risk for so many years, and it was something of a waste of committee time to wrangle over such a simple and obvious idea. Thankfully, we now have a reasonable baseline risk measure to accompany returns, and investors have some means to compare managers on a more equal basis.

I agree with Steve - basically GIPS are a minimum standard, not a maximum. If there are better measures for the product, then include them as well, although atleast ensuring everyone has the SD brings some form of risk measure into the debate rather than potentially not having anything.

As for "n" or "n-1", although n gives the lower answer - it is also the "right" calculation of normal volatility (notwithstanding if there is any such thing as a "correct" risk measure).

The population stat is used when you use all the datapoints of a period, rather than randomly sample some of them and use the sample as a representation of the whole (e.g. you might sample a group of people and use that information as representation of a larger group).

There are 2 points here:

1) taking the last 36 months is not a "random" sample of history - as we are not pretending the last 36 months is a representation of a longer period.

2) the risk you are stating is described as the risk over the last 36 months, so the information IS the population (if you were to randomly take 24 datapoints out of the 36, then use "n-1" as an estimation of the 36 month vol, then that would be fine - but we don't).

I don't see too much controversy here, but sure we will hear more ....

I agree we should strive to present risk and risk adjusted returns in every presentation. I don't agree we should label them as risk. Instead, these information should be presented under a category call "Uncertainly" (I know reader will disagree and the meaning of risk encompass uncertainly).

If we speak to some mom or pop store down the street or maybe Joe The Plumber, what do you think the meaning of risk mean to them? After we trained or educated these potential investors, should we allow them to participate in the market even if these people truly do not understand the meaning of "Risk" in the finance world?

Since most risk numbers are calculated using return series and not holding base, are we not repeating what Lehman hedge fund did? Knowing this could potentially cause misunderstanding to investors, are we truly being fair in our opinion and properly disclosing all the facts/limitations?

GIPS set a minimum standard but there are still investors with limited GIPS understanding. Some US investors favorite questions have been: is my portfolio following GIPS, or has my portfolio been reconciled in accordance to GIPS (rather than GAAP).

First a question for Simon Blakeney.... if I were to use n-1 rather than n, wouldn't it make the risk measure (slightly) forward looking, in which case it would be a benefit? Splitting hairs I know but I'm still curious what you think.

Second I am curious what other firms do to calculate Sharpe ratio as the curriculum from the CIPM program I went through last year states a method different from the one my firm uses. For a 3 year period we would use annualized geometric returns in the numerator and the "standard" standard deviation in the denominator, by "standard" I mean it measures deviations around the arithmetic mean. However the Feibel text from the CIPM curriculum uses annualized arithmetic mean returns in the numerator in order to match the "standard" standard deviation. A footnote states that if geometric returns are used in the numerator, the denominator should be "the standard deviation of the natural log of the single period growth rates".

On the n v n-1, certainly using a smaller number increases the SD, but do not think increasing a number "makes it forward looking" and it is potentially a way that we use statistical terminology to build inappropriate "confidence" to clients rather than concentrating on actually what the information means (and its shortfalls).

From a technical perspective, my understanding of a sample is that it is a random representation of what you are trying to measure, and I do not think the last 36 (say) consecutive months is particularly random. As it is not, then lets represent it as it is and then the user can decide if it is a good predictor for the future etc (rather than think that you have already made some adjustment).

Similarly, I do not think that increasing a number by about 1.5% of its size (for a 36m period) makes it any "more predictive" bearing in mind the normal assumptions it is based upon etc and would rather concentrate on its historical context and looking at investment-horizon relevance for the end investor.

I know it is minor, but do think that we should differentiate facts and estimates if at all possible and clearly define them as such. In the case of historical performance and volatility we have fact, so lets report them like that - rather than making "minor" adjustments that do not add any value and potentially cloud the important information to the end investor.

Some calculates Sharpe Ratio without the risk free return. Certainly, this equation is inappropriate for comparsion purpose and shouldn't be call Sharpe Ratio. If you ask the right question(s), such as: show me the historical Sharpe Ratio, you might be able to see some of the portfolio traits / Characteristics. A better question might be, just show me the monthly returns and I'll calculate the Sharpe Ratio myself.

Spaulding, David Spaulding

About David Spaulding

is an internationally recognized authority on investment performance measurement. He's the founder and Chief Executive Officer of The Spaulding Group, Inc. (www.SpauldingGrp.com), and founder and publisher of The Journal of Performance Measurement. He's the author, contributing author, and co-editor of several investment books. He's actively involved in the investment performance industry, serving on numerous committees and working groups.
Dave earned his BA in Mathematics from Temple University, his MS in Systems Management from the University of Southern California, an MBA in Finance from the University of Baltimore, and a doctorate in Finance and International Economics from Pace University.
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